Atkin-Lehner |
2- 3- 5- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
112140t |
Isogeny class |
Conductor |
112140 |
Conductor |
∏ cp |
288 |
Product of Tamagawa factors cp |
deg |
571392 |
Modular degree for the optimal curve |
Δ |
-1869351372000000 = -1 · 28 · 37 · 56 · 74 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- -4 -6 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-10272,2118436] |
[a1,a2,a3,a4,a6] |
Generators |
[272:-4410:1] [132:1750:1] |
Generators of the group modulo torsion |
j |
-642275344384/10016671875 |
j-invariant |
L |
12.325538127435 |
L(r)(E,1)/r! |
Ω |
0.3961131847392 |
Real period |
R |
0.10804237028992 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001079 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37380i1 |
Quadratic twists by: -3 |